MPC weight problem

[hupo4321]

Hey guys In mpc.cpp file does anyone know how to derivate these two functions 'addSteerWeightR' and 'addSteerWeightF'? I can not understand these two functions.

Looking forward to receiving help!

[HansOersted]

To my understanding, addSteerWeightR and addSteerWeightF penalize the change (or derivative of the change) in the steering angle in the upcoming MPC result and penalize the change in the steering angle between the last MPC and the beginning of the upcoming MPC result.

The best way to understand these two matrices is to expand it.

We will take const Eigen::Matrix2d D = steer_rate_r * (Eigen::Matrix2d() << 1.0, -1.0, -1.0, 1.0).finished(); for example.

This will result in a diagonal matrix below:

Define u = [u1 u2 u3 ...]'
Expand u' * R * u yields
(u1 - u2) ^2 + (u2 - u3) ^2 + (u3 - u4) ^2 + ...

Consequently, the weight for the steering rate compensation is defined in this part.

Likewise, the weight for the steering acceleration is also defined in
const Eigen::Matrix3d D = steer_acc_r * (Eigen::Matrix3d() << 1.0, -2.0, 1.0, -2.0, 4.0, -2.0, 1.0, -2.0, 1.0).finished();

[maxime-clem]

@hupo4321 I marked this as the answer but feel free to ask more questions.